An efficient logarithmic barrier method without line search for convex quadratic programming

S. Chaghoub^a, D. Benterki<sup>b

a</sup> School of Mathematical Science & Institute of Mathematics, Nanjing Normal University, Nanjing 210023, China
^b Université Ferhat Abbas de Sétif

Abstract: In this work, we deal with a convex quadratic problem with inequality constraints. We use a logarithmic barrier method based on some new approximate functions. These functions have the advantage that they allow computing the displacement step easily and without consuming much time contrary to a line search method, which is time-consuming and expensive to identify the displacement step. We have developed an implementation with MATLAB and conducted numerical tests on some examples of considerable size. The obtained numerical results show the accuracy and efficiency of our approach.

Key words: quadratic programming, linear programming, interior point methods, line search, approximate function.

MSC: 90C05, 90C20, 90C25

Received: 13.03.2021
Revised: 15.07.2021
Accepted: 27.01.2022

DOI: 10.15372/SJNM20220207

 English version: Numerical Analysis and Applications, 2022, 15:2, 156–169